5 PSLE Math Question Types That Appear Every Year
These 5 question types show up in PSLE Math every single year. Learn to spot the pattern, pick the right method, and score full marks.
5 PSLE Math Question Types That Appear Every Year
PSLE Math is not random. Year after year, the same five question structures show up in Paper 2 — just wearing different costumes. Learn to recognise them, and you will know exactly what to do before you even pick up your pencil.
Why These 5 Types Matter
Every PSLE Math Paper 2 draws from the same pool of problem structures. The numbers change, the stories change, but the underlying patterns stay the same.
Students who score AL1 do not memorise hundreds of questions. They learn to recognise these five types instantly and match each one to the right method. That is exactly what this guide teaches you.
| # | Question Type | Signal Words | Go-To Method |
|---|---|---|---|
| 1 | Fraction Remainder | ”remainder”, “rest”, “gave away _/_ of…” | Branching |
| 2 | Before-After Ratio | ”at first”, “after giving”, “ratio became” | Constant Part / Total / Difference |
| 3 | Speed, Distance & Time | ”travelled”, “met”, “caught up”, “km/h” | Organise → Formula |
| 4 | Pattern & Sequence | ”figure”, “pattern”, “nth term” | Find the Rule |
| 5 | Excess & Shortage | ”each…gets”, “left over”, “short of” | Assumption Method |
💡 How to Use This Guide
For each type, we show you: (1) how to spot it, (2) the method to use, (3) a full worked example, and (4) the trap to avoid. Read through all five, then practise one type per day.
Type 1: Fraction Remainder Problems
How to Spot It
Look for the word “remainder” or phrases like “the rest”, “what was left”. The question chains two or more fractions together — each one acts on what is left after the previous step.
“Sarah spent 1/4 of her money on a bag. She spent 2/3 of the remainder on shoes. She had $90 left. How much money did she have at first?”
The Method: Branching
Think of the money (or items) as a bar. Each fraction “branches off” a piece. What remains becomes the new whole for the next fraction.
Step-by-step approach:
- Start from the end (the amount left)
- Work backwards through each fraction
- At each step, figure out what fraction of the whole the remainder represents
Worked Example: Sarah's Shopping
Problem:
Sarah spent 1/4 of her money on a bag. She spent 2/3 of the remainder on shoes. She had $90 left. How much money did she have at first?
Step 1: After buying the bag, she had of her money left.
Step 2: She spent of the remainder on shoes, so she kept of the remainder.
Step 3: The \frac13\frac13 \times \frac34\frac14$ of the original.
Step 4: of original = $90, so original = 90 \times 4 = **\360**
✅ Sarah had $360 at first.
❌ Trap: Applying Fractions to the Wrong Whole
The biggest mistake is applying the second fraction to the original amount instead of the remainder. When the question says “2/3 of the remainder”, the denominator is the remainder — not the starting total.
Type 2: Before-After Ratio Problems
How to Spot It
Keywords: “at first”, “after giving”, “after receiving”, “the ratio became”, “ratio was… then became…”
The question gives you a ratio in one state and tells you something changed (transfer, addition, removal). You need to find the original or final amount.
The Method: Identify What Stays Constant
Every before-after ratio problem has something that does not change. Find it, and the problem unlocks.
| What Stays Constant | When It Happens | Example |
|---|---|---|
| Total | Items transferred between two people (no items enter or leave) | “Ali gave Ben 12 marbles” |
| Difference | Both quantities change by the same amount | ”Both received 6 sweets each” |
| One Part | Only one person’s quantity changes | ”Cindy spent $40” (David’s money unchanged) |
Worked Example: Marble Transfer
Problem:
Ali and Ben had marbles in the ratio 5 : 3. After Ali gave Ben 12 marbles, the ratio became 1 : 1. How many marbles did they have altogether?
Step 1: What stays constant? Ali gives to Ben — no marbles enter or leave. The total stays the same.
Step 2: Before → 5 : 3 → total = 8 units. After → 1 : 1 → total = 2 units. Make the totals equal: multiply the “after” ratio by 4 → 4 : 4 (total = 8 units).
Step 3: Ali went from 5 units to 4 units → Ali lost 1 unit. That 1 unit = 12 marbles.
Step 4: 1 unit = 12 marbles. Total = 8 units = = 96 marbles
✅ They had 96 marbles altogether.
❌ Trap: Forgetting to Make Units Equal
Before = 5 : 3 (8 units), After = 1 : 1 (2 units). These “units” are different sizes. You must scale one ratio so the constant quantity (total, difference, or one part) uses the same number of units in both ratios. Skip this step and the entire answer falls apart.
Type 3: Speed, Distance & Time Problems
How to Spot It
Keywords: “km/h”, “m/min”, “travelled”, “left at”, “met along the way”, “caught up”. The question involves movement — one or two people/vehicles, with distances or times to figure out.
The Method: Organise First, Calculate Second
Speed questions trip students up because there is a lot of information. The key is to organise everything into a table before doing any calculation.
| Speed | Time | Distance | |
|---|---|---|---|
| Person A | ? | ? | ? |
| Person B | ? | ? | ? |
Then apply: Distance = Speed × Time
Worked Example: Meeting Problem
Problem:
Town A and Town B are 180 km apart. Car X leaves Town A at 08:00 travelling at 60 km/h towards Town B. Car Y leaves Town B at 08:30 travelling at 80 km/h towards Town A. At what time do they meet?
Step 1: Car X has a 30-minute head start. In 30 min, Car X covers km.
Step 2: At 08:30, remaining distance = km. Now both cars are moving towards each other.
Step 3: Combined speed = km/h.
Step 4: Time to meet = hours = 1 hour 4 minutes (rounded to nearest minute).
Step 5: 09:34
✅ They meet at 09:34.
Speed, Distance & Time Calculator
Cover what you want to find. The remaining shows the formula!
Cover S → D ÷ T
❌ Trap: Wrong Combined Speed Direction
When two objects move towards each other, add their speeds. When they move in the same direction (catching up), subtract. Mixing this up is the #1 speed question mistake.
⚠️ Watch Your Units
If speed is in km/h but time is given in minutes, convert minutes to hours first (divide by 60). Never mix units in the same formula.
Type 4: Pattern & Sequence Questions
How to Spot It
Keywords: “figure”, “pattern”, “how many in the nth figure”, “what is the 100th number”. The question shows 3–4 figures or numbers and asks you to find a later term or the total.
The Method: Build a Table, Find the Rule
Don’t try to see the pattern in your head. Write it out in a table and look for a relationship between the figure number and the value.
Worked Example: Dot Pattern
Problem:
Figure 1 has 4 dots. Figure 2 has 10 dots. Figure 3 has 18 dots. Figure 4 has 28 dots. How many dots are in Figure 10?
Step 1: Build a table.
| Figure | Dots | Difference |
|---|---|---|
| 1 | 4 | — |
| 2 | 10 | +6 |
| 3 | 18 | +8 |
| 4 | 28 | +10 |
Step 2: The differences are 6, 8, 10… They increase by 2 each time. So the next differences are 12, 14, 16, 18, 20, 22.
Step 3: Continue the table:
| Figure | +Difference | Dots |
|---|---|---|
| 5 | +12 | 40 |
| 6 | +14 | 54 |
| 7 | +16 | 70 |
| 8 | +18 | 88 |
| 9 | +20 | 108 |
| 10 | +22 | 130 |
✅ Figure 10 has 130 dots.
💡 Shortcut: Look at the Second Difference
If the first differences are not constant but the second differences are (like +2, +2, +2 above), the pattern follows a quadratic rule. For PSLE, you usually do not need the formula — just extend the table. But knowing this tells you the differences will keep growing steadily.
❌ Trap: Assuming a Constant Difference
Not every pattern has a constant difference. Students who see 4, 10, 18 and assume “+6 every time” will write 4, 10, 16, 22… and get it completely wrong. Always check at least 3 differences before deciding the rule.
Type 5: Excess & Shortage (Assumption Method)
How to Spot It
Keywords: “if each… gets”, “left over”, “not enough”, “short of”. The question describes distributing items two different ways and gives the leftover or shortage each time.
“If each child gets 5 sweets, there are 3 left over. If each child gets 7 sweets, there are 5 short. How many children are there?”
The Method: Assumption Method
- Assume one distribution and calculate the total
- Compare with the other distribution
- The difference in totals divided by the difference per person gives you the answer
Worked Example: Sweet Distribution
Problem:
If each child gets 5 sweets, there are 3 left over. If each child gets 7 sweets, there are 5 sweets short. How many children are there?
Step 1: The difference between giving 5 and giving 7 = 2 extra sweets per child.
Step 2: In Scenario 1, there are 3 extra. In Scenario 2, there are 5 short. Total difference in sweets = .
Step 3: Number of children = 4 children
Check: Total sweets = . Check: , short by . ✓
✅ There are 4 children.
💡 Excess + Shortage = Add. Both Excess = Subtract.
If one scenario has a leftover and the other has a shortage, add them for the total difference. If both scenarios have a leftover (or both have a shortage), subtract instead.
❌ Trap: Confusing Excess with Shortage
Read carefully: “3 left over” means excess. “5 short” means shortage. If the question says “needs 5 more”, that is a shortage. Mixing these up flips your addition to subtraction and gives the wrong answer.
Your 5-Day Practice Plan
Now that you know all five types, here is how to lock them in before your exam.
| Day | Type to Practise | What to Do |
|---|---|---|
| Monday | Fraction Remainder | Do 5 questions. Focus on identifying which fraction acts on which remainder. |
| Tuesday | Before-After Ratio | Do 5 questions. For each one, write down what stays constant (total, difference, or one part). |
| Wednesday | Speed, Distance & Time | Do 5 questions. Fill in a table for every question before calculating anything. |
| Thursday | Pattern & Sequence | Do 5 questions. Always build a difference table — never guess the pattern. |
| Friday | Excess & Shortage | Do 5 questions. Practise deciding when to add vs subtract the differences. |
💡 Weekend Challenge
On Saturday, do a mixed set of 10 questions covering all 5 types. For each question, write down which type it is before you start solving. This trains your pattern recognition — the real skill that separates AL1 from AL3.
Quick-Reference Cheat Sheet
Save this for your revision:
| Type | Signal Words | Method | Key Formula / Rule |
|---|---|---|---|
| Fraction Remainder | ”remainder”, “rest” | Branching (work backwards) | Fraction of remainder × fraction of original |
| Before-After Ratio | ”at first”, “ratio became” | Make constant quantity equal | Scale ratios → find 1 unit |
| Speed, Distance & Time | ”km/h”, “met”, “caught up” | Table → formula | D = S × T |
| Pattern & Sequence | ”figure”, “pattern”, “nth” | Difference table | Check 1st and 2nd differences |
| Excess & Shortage | ”left over”, “short of” | Assumption method | Total diff ÷ diff per person |
What Examiners Actually Reward
Knowing the method is only half the battle. Here is what earns full marks:
-
Show the reasoning, not just the numbers. Write “Remainder = ” not just "". The examiner needs to see what each line represents.
-
Label your units. $360, not 360. 96 marbles, not 96. Missing units can cost you 1 mark.
-
Write a statement answer. End with a sentence: “Sarah had $360 at first.” This proves you answered the right question.
-
Draw models when the question involves comparison. Bar models are not just for learning — they earn you method marks in the exam.
⚠️ The 'Right Method, Wrong Answer' Problem
If your method is correct but you make a calculation error, you still earn method marks (M marks). But only if the examiner can follow your working. Messy or skipped steps mean no partial credit. Always show every step clearly — it is your insurance policy.
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